64 citations · 387 across the 46 of their papers we have counts for
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math.DS2014
On the relative coexistence of fixed points and period-two solutions near border-collision bifurcations
David J. W. Simpson
At a border-collision bifurcation a fixed point of a piecewise-smooth map intersects a surface where the functional form of the map changes. Near a generic border-collision bifurca…
math.DS2014★ 14 cited
Stochastic Perturbations of Periodic Orbits with Sliding
David J. W. Simpson, Rachel Kuske
Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a di…
math.DS2014★ 13 cited
Scaling laws for large numbers of coexisting attracting periodic solutions in the border-collision normal form
David J. W. Simpson
A wide variety of intricate dynamics may be created at border-collision bifurcations of piecewise-smooth maps, where a fixed point collides with a surface at which the map is nonsm…